IACR paper details

In this paper we present a general framework for password-based
authenticated key exchange protocols, in the common reference
string model. Our protocol is actually an abstraction of the key
exchange protocol of Katz et al.\ and is based on the recently
introduced notion of smooth projective hashing by Cramer and
Shoup. We gain a number of benefits from this abstraction. First,
we obtain a modular protocol that can be described using just
three high-level cryptographic tools. This allows a simple and
intuitive understanding of its security. Second, our proof of
security is significantly simpler and more modular. Third, we are
able to derive analogues to the Katz et al.\ protocol under
additional cryptographic assumptions. Specifically, in addition to
the DDH assumption used by Katz et al., we obtain protocols under
both the Quadratic and $N$-Residuosity assumptions. In order to
achieve this, we construct new smooth projective hash functions.